In this paper, we adopt a finite strain constitutive model in an integrated algorithmic numerical scheme to describe the thermomechanical behaviour of shape memory alloys (SMA). The constitutive model is assumed to follow classical plasticity theory in its formulation. An explicit meshfree formulation is constructed to accurately describe the response of SMAs under complex loading paths and a nonlinear meshfree procedure is developed for their numerical simulation. Controlled cyclic mechanical loading tests are performed on two commercial Nitinol (NiTi) wires and the response was compared with predictions from the meshfree simulations. The unique response of these Nitinol wires under mechanical loads are observed and explained.